A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac’s delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz...

Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted L−algebra L ω (G). Here, we establish necessary and sufficient conditions for L ω (G) to be φ−contractible, pseudo-contractible or contractible. Moreover we give some similar results about L(G,ω).

In terms of applications, the min discrepancy problem appears in many varied areas of both Computer Science (Computational Geometry, Comb. Optimization, Monte-Carlo simulation, Machine learning, Complexity, Pseudo-Randomness) and Mathematics (Dynamical Systems, Combinatorics, Mathematical Finance, Number Theory, Ramsey Theory, Algebra, Measure Theory,...). One may consult any of the following b...

We present a package for Mathematica computer algebra system which allows the exploitation of local files as sources of random data. We provide the description of the package and illustrate its usage by showing some examples. We also compare the provided functionality with alternative sources of randomness, namely a built-in pseudo-random generator and the package for accessing hardware true ra...

Let G be a Lie group, G its Lie algebra, T G its cotangent bundle and D := tG the Lie algebra of T G. We investigate the group of automorphisms of D. More precisely, we fully characterize the space of all derivations of D. As a byproduct, we also characterize some spaces of operators on G amongst which the space J of bi-invariant tensors on G and prove that if G has a bi-invariant Riemannian or...

In this paper, we introduce two classes of localized integral operators on L2(Rd) with the Wiener class W and the Kurbatov class K of integral operators as their models. We show that those two classes of localized integral operators are pseudo-inverse closed non-unital subalgebra of B2, the Banach algebra of all bounded operators on L2(Rd) with usual operator norm.

In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantisation given by the representation theory. They form an algebra of operators which shares many properties with the...

In this paper, the second in a series of eight we continue our development of the basic tools of the multivector and extensor calculus which are used in our formulation of the differential geometry of smooth manifolds of arbitrary topology. We introduce metric and gauge extensors, pseudo-orthogonal metric extensors, gauge bases, tetrad bases and prove the remarkable golden formula, which permit...

We consider Bézier-like formulas with weights in quaternion and geometric (Clifford) algebra for parametrizing rational curves and surfaces. The simplest non-trivial quaternionic case of bilinear formulas for surface patches is studied in detail. Such formulas reproduce well known biquadratic parametrizations of principal Dupin cyclide patches, and are characterized in general as special Darbou...